信息论基础
2012-7
科学出版社
杨伟豪
412
430000
《信息论基础(英文版)》作者（杨伟豪）现为香港中文大学网络编码研究所主任，是网络编码理论的提出者之一。本书原版自2002年出版以来，被哥伦比亚大学、康奈尔大学、麻省理工学院、斯坦福大学等美国著名学府所采用，是信息理论方面的重要教材。本书首先介绍了信息论的经典内容，然后全面详细地论述了，度量、网络编码、Shannon型与非Shannon型信息不等式等理论，以及熵函数与群论之间的关系。《信息论基础(英文版)》中配有大量的实例、插图和习题，适合作为通信、电子信息、计算机等专业的高年级本科生和研究生的教材，也可供相关领域的科研人员参考。
杨伟豪(Raymond
w．Yeung)教授1988年毕业于美国康奈尔大学。获博士学位。之后曾在AT&T贝尔实验室工作3年，于1
991年加入香港中文大学，现为网络编码研究所主任，是网络编码理论的提出者之一，其主要研究领域为信息理论与网络编码。他还是IEEE
Fellow和香港工程师学会会士。
1. THE SCIENCE OF INFORMATION
2. INFORMATION MEASURES
2.1 Independence and Markov Chai
2.2 Shannon's Information Measures
2.3 Continuity of Shannon's Information Measures
2.4 Chain Rules
2.5 Informational Divergence
2.6 The Basic Inequalities
2.7 Some Useful Information Inequalities
2.8 Fano's Inequality
2.9 Entropy Rate of Stationary Source
Problems
Historical Notes
3. ZERO-ERROR DATA COMPRESSION
3.1 The Entropy Bound
3.2 Prefix Codes
3.2.1 Definition and Existence
3.2.2 Huffman Codes
3.3 Redundancy of Prefix Codes
Problems
Historical Notes
4. WEAK TYPICALITY
4.1 The Weak AEP
4.2 The Source Coding Theorem
4.3 Efficient Source Coding
4.4 The Shannon-McMiilan-BreimanTheorem
Problems
Historical Notes
5. STRONG TYPICALITY
5.1 StrongAEP
5.2 Strong Typicality Veus Weak Typicality
5.3 Joint Typicality
5.4 An Interpretation of the Basic Inequalities
Problems
Historical Notes
6. THE/-MEASURE
6.1 Preliminaries
6.2 The/-Measure for Two Random Variables
6.3 Cotruction of the/-Measure ч*
6.4 #* Can be Negative
6.5 Information Diagrams
6.6 Examples of Applicatio
Appendix 6.A: A Variation of the Inclusion-Exclusion Formula
Problems
Historical Notes
7. MARKOV STRUCTURES
7.1 Conditional Mutual Independence
7.2 Full Conditional Mutual Independence
7.3 Markov Random Field
7.4 Markov Chain
Problems
Historical Notes
8. CHANNEL CAPACITY
8.1 Discrete MemorylessChannels
8.2 The Channel Coding Theorem
8.3 The Convee
8.4 Achievability of the Channel Capacity
8.5 A Discussion
8.6 Feedback Capacity
8.7 Separation of Source and Channel Coding
Problems
Historical Notes
9. RATE-DISTORTION THEORY
9.1 Single-Letter Distortion Measures
9.2 The Rate-Distortion Function R(D)
9.3 The Rate-Distortion Theorem
9.4 The Convee
9.5 Achievability of RI(D)
Problems
Historical Notes
10. THE BLAHUT-ARIMOTO ALGORITHMS
10.I Alternating Optimization
10.2 The Algorithms
10.2.1 Channel Capacity
10.2.2 The Rate-Distortion Function
10.3 Convergence
10.3.1- A Sufficient Condition
10.3.2 Convergence to the Channel Capacity
Problems
Historical Notes
11. SINGLE-SOURCE NETWORK CODING
11.1 A Point-to-Point Network
11.2 What is Network Coding?
11.3 A Network Code
11.4 The Max-Flow Bound
11.5 Achievability of the Max-Flow Bound
11.5.1 Acyclic Networks
11.5.2 Cyclic Networks
Problems
Historical Notes
12. INFORMATION INEQUALITIES
12.1 The Region Fn
12.2 Information Expressio in Canonical Form
12.3 A Geometrical Framework
12.3.1 Uncotrained Inequalities
12.3.2 Cotrained Inequalities
12.3.3 Cotrained Identities
12.4 Equivalence of Cotrained Inequalities
12.5 The Implication Problem of Conditional Independence
Problems
Historical Notes
13 SHANNON-TYPE INEQUALITIES
13.1 The Elemental Inequalities
13.2 A Linear Programming Approach
13.2.1 Uncotrained Inequalities
13.2.2 Cotrained Inequalities and Identities
13.3 A Duality
13.4 Machine Proving - ITIP
13.5 Tackling the Implication Problem
13.6 Minimality of the Elemental Inequalities
Appendix 13.A: The Basic Inequalities and the Polymatroidal
Axioms
Problems
Historical Notes
14. BEYOND SHANNON-TYPE INEQUALITIES
14.1 Characterizatio of г2,г3, and гn
14.2 A Non-Shannon-Type Uncotrained Inequality
14.3 A Non-Shannon-Type Cotrained Inequality
14.4 Applicatio
Problems
Historical Notes
15. MULTI-SOURCE NETWORK CODING
15.1 Two Characteristics
15.1.1 The Max-Flow Bounds
15.1.2 Superposition Coding
15.2 Examples of Application
15.2.1 Multilevel Diveity Coding
15.2.2 Satellite Communication Network
15.3 A Network Code for Acyclic Networks
15.4 An Inner Bound
15.5 An Outer Bound
15.6 The LP Bound and Its Tightness
15.7 Achievability of Rin
Appendix 15.A: Approximation of Random Variables with
Infinite Alphabets
Problems
Historical Notes
16. ENTROPY AND GROUPS
16.1 Group Preliminaries
16.2 Group-Characterizable Entropy Functio
16.3 A Group Characterization of гn
16.4 Information Inequalities and Group Inequalities
Problems
Historical Notes
Bibliography
Index
